The key to the success of the CES methodology is founded
on ensemble Kalman methods and the cheap derivative-free
manner in which they can learn states or, in the setting
of this paper, parameters, from data. We emphasize that
there exists already significant work showing, empirically,
that ensemble Kalman methods can be generalized to perform
uncertainty quantification beyond the Gaussian
setting [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}
by means of iterated EnKF, which may be motivated via the Newton
method [4]}, and also by means of ensemble-based Gauss-Newton
[9]} in the presence of model error.
However, it is unclear how this methodology might be rigorously justified and developed as a general-purpose
tool, despite the empirical successes it has shown on a number of
challenging problems. In contrast,
CES may be systematically refined, based on the theory of
Gaussian process emulation [10]} and its use
within Bayesian inference [11]}. CES does not depend on the
UQ properties of ensemble methods, only on their optimization
and estimation properties, which are amenable to systematic analysis
[12]}, [13]}, [14]}. For these reasons, CES has considerable potential as a systematic approach to uncertainty quantification.
